GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Nov 2018, 03:30

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

Two trains, X and Y, started simultaneously from opposite ends of a 10

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50661
Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post Updated on: 01 Oct 2018, 01:04
1
16
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:44) correct 25% (02:04) wrong based on 1311 sessions

HideShow timer Statistics

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


The Official Guide For GMAT® Quantitative Review, 2ND Edition

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics


Originally posted by Bunuel on 30 Nov 2010, 05:30.
Last edited by Bunuel on 01 Oct 2018, 01:04, edited 3 times in total.
Renamed the topic and edited the question.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50661
Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 27 Feb 2014, 06:06
5
61
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

As the ratio of the rates of X and Y is 3 to 5 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 3/(3+5)=3/8 of 100 miles: 100*3/8=37.5 miles.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT ToolKit User
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 27 Feb 2014, 21:05
21
16
Train X's Average speed = 100/5 = 20 mph
Train Y's Average speed = 100/3 mph
Relative speed when trains travel toward each other = 20 + 100/3 = 160/3 mph.

Note that the 2 trains together would have traveled 100 miles at their meeting junction. Also, the time traveled for both trains would be the same at the meeting point.

Thus, Time = 100/(160/3) = 30/16 = 15/8 hours

Of the 100 miles, Distance covered by Train A = 20mph * 15/8 hours = 37.5 miles.

Ans is (A).
General Discussion
Manager
Manager
User avatar
Joined: 01 Nov 2010
Posts: 128
Location: Zürich, Switzerland
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 30 Nov 2010, 09:34
4
1
Train A speed = t1 = 20 mph
Train B speed= t2 = 100/3 mph
Combined speed(travelling towards each other) = 160/3 mph

When trains meet each other, they've covered 100 miles together.

Thus time = 100/(160/3) = 30/16 = 15/8 hours

out of 100 miles, distance covered by Train A = 20mph * 15/8 hours = 37.5 miles
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8560
Location: Pune, India
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 30 Nov 2010, 09:59
19
8
ajit257 wrote:
Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ?


Can someone please explain the concept behind this type of problem ? All help appreciated.


The concept used in these questions is Relative Speed.

If two people walk in opposite directions (either towards each other or away from each other), their speed relative to each other is the sum of their speeds. e.g. If you are walking away from me at a speed of 2 miles/hr and I am walking away from you at a speed of 1 mile/hr, together we are creating a distance of 3 miles in 1 hr between us so our relative speed is 2 + 1 = 3 miles/hr
On the other hand, when two people walk in the same direction, their relative speed is the difference between their speeds.
e.g. if you are walking away from me at 1 mile/hr and I am walking towards you at 2 miles/hr, my speed relative to you is 2-1 = 1 mile/hr.

Time taken to meet = Total distance traveled/Relative speed

Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 miles/hr
Relative Speed = 20 + 100/3 = 160/3 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(160/3) hr = 15/8 hrs

In this time, train X would have traveled 20 * (15/8) = 37.5 miles

Faster Alternate Approach using Ratios :

Time taken by train X : Time taken by train Y = 5:3
Then, Speed of train X:Speed of train Y = 3:5
Since they start simultaneously, they travel for same time. So the ratio of their distance covered should be same as ratio of their speeds.
Distance covered by train X : Distance covered by train Y = 3:5
3/8 *100 = 37.5 miles (Distance covered by train X)
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 530
CAT Tests
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 17 Feb 2011, 11:12
3
Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

I solved as under
Time taken to meet = Total distance traveled/Relative speed

Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 miles/hr
Relative Speed = 20 + 100/3 = 160/3 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(160/3) hr = 15/8 hrs

In this time, train X would have traveled 20 * (15/8) = 37.5 miles
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8560
Location: Pune, India
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 17 Feb 2011, 18:33
2
Baten80 wrote:
Two trains X and Y started simultaneously from opposite ends of a 100 mile route and travelled toward each other on parallel tracks. Train X travelling at a constant rate completed the 100 mile trip in 5 hours. Train Y travelling at constant rate completed the 100 mile trip in 3 hours. How many miles had train X travelled when it met train Y ?
(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

I solved as under
Time taken to meet = Total distance traveled/Relative speed

Speed of train X = 100/5 = 20 miles/hr
Speed of train Y = 100/3 miles/hr
Relative Speed = 20 + 100/3 = 160/3 miles/hr
Distance between them = 100 miles
Time taken to meet = 100/(160/3) hr = 15/8 hrs

In this time, train X would have traveled 20 * (15/8) = 37.5 miles


Another approach:
Time taken by train X to cover 100 miles : Time taken by train Y to cover 100 miles = 5:3
Therefore, Speed of X: Speed of Y = 3:5
So, when they meet, X would have covered (3/8)th of the total distance of 100 miles.
Distance covered by X = (3/8)*100 = 37.5 miles
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 27 Feb 2014, 23:31
5
1
Answer = (A) 37.5

Explaination:

Let the point where they meet is x kms from Point X

So it is (100-x) from point Y

Ratio of distance = Ratio of time taken

x/(100-x) = 20 / (100/3)

Solving the above equation, we get x = 37.5
Attachments

sepp.jpg
sepp.jpg [ 24.24 KiB | Viewed 17855 times ]


_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
B
Joined: 30 Jul 2013
Posts: 62
Concentration: Technology, General Management
GMAT Date: 07-03-2015
GPA: 3.8
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 29 May 2015, 20:40
1
As per the OG explanations:

To solve this problem, use the formula distance = rate x time and its two equivalent forms rate = distance and time = distance. Train X time rate traveled 100 miles in 5 hours so ts rate was 100/5 = 20 miles per hour. Train Y traveled 100 miles in 3 hours so its rate was 1003 miles per hour. If t represents the number of hours the trains took to meet, then when the trains met, Train X had traveled a distance of 20t miles and Train Y had traveled a distance of 100/3 t miles.

How can "t" represent the time for both the trains? Because they have different rates, doesn't that mean each will take different time to meet?

Please explain.
_________________

On the Kudos Spree.

If you like my post/comment please appreciate with kudos :)

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12883
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 30 May 2015, 14:55
Hi Pretz,

In this question, the variable "T" represents "amount of time that each train was moving" - since both trains started moving SIMULTANEOUSLY, the "T" can be used in both calculations ("T" does NOT represent the "time of day"). Since the trains are moving at DIFFERENT RATES, the DISTANCE that each train will travel will be different.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8560
Location: Pune, India
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 31 May 2015, 23:43
2
Pretz wrote:
As per the OG explanations:

To solve this problem, use the formula distance = rate x time and its two equivalent forms rate = distance and time = distance. Train X time rate traveled 100 miles in 5 hours so ts rate was 100/5 = 20 miles per hour. Train Y traveled 100 miles in 3 hours so its rate was 1003 miles per hour. If t represents the number of hours the trains took to meet, then when the trains met, Train X had traveled a distance of 20t miles and Train Y had traveled a distance of 100/3 t miles.

How can "t" represent the time for both the trains? Because they have different rates, doesn't that mean each will take different time to meet?

Please explain.



Think of it this way:

You are at your home and your friend is at his home. You both decide to meet. You leave your respective homes at exactly 12:00 and then travel toward each other's homes at your own speeds. You meet i.e. reach the same point, at say, 12:20. Have you traveled for the same amount of time? Sure. You both have traveled for exactly 20 mins. You traveled at your own speeds: say you are very fast and your friend is very slow. So how does this impact the entire equation? You would have covered much more distance than your friend in the same 20 mins. So higher speed will lead to more distance covered but the time for which the two of you would have traveled would be the same. Similarly, since the trains start at the same time, when they meet, the time elapsed would be the same. They will cover different distances due to their different speeds.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
User avatar
Joined: 18 Aug 2014
Posts: 119
Location: Hong Kong
Schools: Mannheim
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 18 Jun 2015, 03:15
2
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



Is this approach recommendable?:

speed x = 100/5 = 20mph
speed y = 100/3 = 33,3mph

after 1h: X = 20miles, Y = 33,3 miles
after 2h: X= 40 miles, Y = 66,6 miles --> together 106,6 miles ... total dist = 100 miles..they have met in this time frame!
as 106,6 miles, X traveled not 40 but slightly lower --> 37,5 --> Answer A
CEO
CEO
User avatar
P
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2701
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 18 Jun 2015, 03:45
LaxAvenger wrote:
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Problem Solving
Question: 119
Category: Algebra Applied problems
Page: 77
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



Is this approach recommendable?:

speed x = 100/5 = 20mph
speed y = 100/3 = 33,3mph

after 1h: X = 20miles, Y = 33,3 miles
after 2h: X= 40 miles, Y = 66,6 miles --> together 106,6 miles ... total dist = 100 miles..they have met in this time frame!
as 106,6 miles, X traveled not 40 but slightly lower --> 37,5 --> Answer A


Yes, It's absolutely correct approximation with the given options.

Instead you could have done another thing here

Distance of X/Distance of Y = speed of X/speed of Y

a/(100-a) = 20/33.3

a/(100-a) = 6/10

10a = 600-6a

16a = 600

a = 37.5
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Retired Moderator
avatar
Joined: 29 Oct 2013
Posts: 265
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)
GMAT ToolKit User
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 01 Feb 2016, 20:17
3
No calculations approach.
By the end of hr1 A would’ve traveled 20 miles and B 33 1/3 miles. So they have not met yet
By the end of hr2 A would’ve traveled 40 miles and B 66 2/3 miles. So they have already crossed. Thus A traveled less than 40 miles when it first met B. The only choice less than 40 miles is A
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

Senior Manager
Senior Manager
User avatar
S
Joined: 08 Dec 2015
Posts: 294
GMAT 1: 600 Q44 V27
Reviews Badge
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 07 Feb 2017, 04:26
Bunuel isn't the ratio of X to Y suppose to be 5 : 3 and not 3 to 5?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50661
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 07 Feb 2017, 05:05
2
iliavko wrote:
Bunuel isn't the ratio of X to Y suppose to be 5 : 3 and not 3 to 5?


Train X, travelling at a constant rate, completed the 100-mile trip in 5 hours --> rate of X = (distance)/(time) = 100/5 =20 miles per hour;
Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours --> rate of Y = (distance)/(time) = 100/3 miles per hour;

(rate of X)/(rate of Y) = 20/(100/3) = 20*3/100 = 3/5.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 09 Feb 2017, 16:29
2
1
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5


We are given that train X completed the the 100-mile trip in 5 hours, and that train Y completed the 100-mile trip in 3 hours.

Since rate = distance/time, the rate of train X is 100/5 = 20 mph and the rate of train Y is 100/3 mph.

Since the trains left at the same time, we can let the time of each train = t.

We need to determine the distance traveled by train X when it met train Y. Since the two trains are “converging” we can use the formula:

distance of train X + distance of train Y = total distance

20t + (100/3)t = 100

Multiplying the entire equation by 3, we have:

60t + 100t = 300

160t = 300

t = 300/160 = 30/16 = 15/8.

Thus, train X and Y met each other after 15/8 hours.

Since distance = rate x time, the distance traveled by train X when it met train Y was:

15/8 x 20 = 300/8 = 75/2 = 37.5 miles.

Answer: A
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 629
Location: India
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 30 May 2017, 16:17
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

1. They would have met in 100/(100/5+100/3) hrs =15/8 hrs
2. In that time X would have traveled, Time *speed =15/8 *20=37.5
_________________

Srinivasan Vaidyaraman
Sravna Holistic Solutions
http://www.sravnatestprep.com

Holistic and Systematic Approach

Manager
Manager
User avatar
S
Joined: 22 Nov 2016
Posts: 213
Location: United States
Concentration: Leadership, Strategy
GPA: 3.4
Reviews Badge
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 25 Jun 2017, 14:31

I like to sketch out the problem and many times it is a fast method.



As you can see train A meets train B somewhere between the 20 and 40th mile. Looking at the answer choices, it is pretty obvious that A is the answer.
Attachments

rest.jpg
rest.jpg [ 19.09 KiB | Viewed 1980 times ]


_________________

Kudosity killed the cat but your kudos can save it.

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10  [#permalink]

Show Tags

New post 07 Dec 2017, 09:24
Top Contributor
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5



Train X completed the 100-mile trip in 5 hours
Speed = distance/time
= 100/5
= 20 mph

Train Y completed the 100-mile trip in 3 hours
Speed = distance/time
= 100/3
33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y?
Let's start with a word equation.

When the two trains meet, each train will have been traveling for the same amount of time
So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed
We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels
So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation.
We get: d/20 = (100 - d)/33
Cross multiply to get: (33)(d) = (20)(100 - d)
Expand: 33d = 2000 - 20d
Add 20d to both sides: 53d = 2000
So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40
Since the denominator is greater than 50, we can conclude that 2000/53 is LESS THAN 40
Since only one answer choice is less than 40, the correct answer must be A

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com
Image

GMAT Club Bot
Re: Two trains, X and Y, started simultaneously from opposite ends of a 10 &nbs [#permalink] 07 Dec 2017, 09:24

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

Two trains, X and Y, started simultaneously from opposite ends of a 10

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.